The broad, long-term objectives of this proposal are to develop better statistical approaches for mapping genes influencing complex diseases in humans and mice. To this end, we plan to extend and refine existing models and methods, as well as to develop novel approaches. We will use likelihood methods that seek to exploit the increased power of linkage analysis with multilocus marker data and multilocus models to the greatest extent possible. The three specific aims of this proposal fall into three areas. A. Novel likelihood-based methods for the linkage analysis of complex quantitative human traits. In recent research, we have found that score tests in the unknown recombination fraction between a marker and a disease-susceptibility locus generally have good power to detect linkage in sib pairs. We aim to develop these tests further so as to be suitable for use with data from different sets of relatives, and for the joint analysis of traits believed to be affected by the same genes. B. Multi-locus models and methods for experimental crosses. We plan to use a model selection approach to search for segregating genes which interact to produce complex disease phenotypes differences in cross between inbred strains of mice. Simulation of mouse chromosomes will play a key role in the evaluation of this new strategy. C. Multi-locus analyses for large pedigrees. Existing methods for carrying out multi-locus mapping on pedigrees have known limitations. We plan to produce algorithms which combine the elements of the best approach for large pedigrees (the Elston-Steward algorithm) with those of the best approach for a large number of loci (the Lander-Green algorithm). We will build on recent engineering research on Hidden Markov Models for 2-dimensional Markov random fields.